The invention relates to an arrangement for affixing a bottom in a cylindrically shaped container made of thermoplastic synthetic material, which bottom has an edge portion adapted to be inserted or fastened onto the cylindrical container. The bottom is also made of thermoplastic material and is affixed by means of a rotatably mounted counter pressure member which coacts with a sonotrode (ultrasonic welding maching) which acts as a welding head. It is already known to effect welding connections by means of ultrasonic-welding heads acting on thermoplastic objects. It is an object of this invention to provide an arrangement which permits to carry out such a welding process for affixing an insertable bottom having a connecting edge onto a thin-walled cylindrical container having little or no inherent rigidity without deforming this container while nevertheless attaining a fluid-tight connection.